Debian / Ubuntu

Debian

The best way to get up-to-date GNUstep packages is to upgrade from stable to testing or unstable. If upgrading to Debian unstable is not desirable it is possible to simply add the unstable apt lines to the sources.list and specify the distribution when installing the packages, e.g.

# apt-get install -t unstable gnumail.app

This method might upgrade some other packages to satisfy dependencies, but will have a much smaller impact on the system since only the packages on which GNUstep depends will be upgraded.

Ubuntu

As Ubuntu is Debian-based you can likewise install gnustep libraries (and their dependencies) via

sudo apt-get install gnustep gnustep-devel

apt will also suggest a lot of apps to install.

Install from source: Dependencies

If you want to compile from source install the following Dependencies packages (applies to both Debian and Ubuntu):

Gentoo

For a list of GNUstep-related ebuilds, see the Online Package Database.
For the most recent packages, type ACCEPT_KEYWORDS="~x86" emerge package-name (or analogically for your cpu family: "~sparc", "~ppc" ...)

Slackware

Version 10.2

Libraries and accompanying applications will build with no modifications. Slackware 10.2 ships with GCC 3.3.6, so mixed Objective-C and C++ code is not supported, meaning additional frameworks/libraries may not be supported.

Version 11.0

This version of Slackware works the same as the previous (10.2). Libraries and applications will build with no modifications, but due to the GCC version used (3.4.6) Objective-C++ is not supported.

Version 12.0

GNUstep compiles and install on Slackware 12.0 perfectly. Unfortunately, this version of Slackware does not include an Objective-C++ compiler.

Packages

Build Scripts

SuSE

Packages for GNUstep releases can be found on the Open Build Service (OBS).

Version 11.3

The package of pixman that comes with OpenSuse 11.3 seems to be broken for some graphic drivers. You may either downgrade or upgrade to another version of pixman (plus cairo) or use a different GNUstep backend.
For me upgrading to the cairo version as provided by the GNOME Factory project on the OpenSuse Build Service worked perfectly. [1]